Simplify the following expression: $ n = \dfrac{-5x}{x - 5} + \dfrac{-10}{7} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{-5x}{x - 5} \times \dfrac{7}{7} = \dfrac{-35x}{7x - 35} $ Multiply the second expression by $\dfrac{x - 5}{x - 5}$ $ \dfrac{-10}{7} \times \dfrac{x - 5}{x - 5} = \dfrac{-10x + 50}{7x - 35} $ Therefore $ n = \dfrac{-35x}{7x - 35} + \dfrac{-10x + 50}{7x - 35} $ Now the expressions have the same denominator we can simply add the numerators: $n = \dfrac{-35x - 10x + 50}{7x - 35} $ $n = \dfrac{-45x + 50}{7x - 35}$